We report on the observation of the HI filament LVC 88+36-2 with the Deep Survey/Spectrometers of EUVE. Detecting the shadow of this cloud in absorption might have proven the existence of a diffuse EUV background behind the cloud, and constrain the emission geometries of the hot plasma in the Local Interstellar Medium (LISM). By detecting diffuse emission in the EUVE spectrometers, it would also be possible to constrain the temperature and pressure of the emitting regions as well as determine whether or not the hot phase of the LISM is in equilibrium with cosmic elemental abundances. Unfortunately, we did not detect a cloud shadow with this set of observations. This is due to a combination of circumstances, but mostly due to the fact that EUV diffuse emission is weak compared to the background levels of EUVE. If a shadow exists in the EUVE, then it is less than 1% of the EUVE detector background of 1e-3 cts arcmin(exp -2) in the Deep Survey detector.